Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

Opening

10 minutes

At the start of today's class, I explain to students that they will be applying the concepts and skills learned during this unit to investigate and model the the vertical jumping ability of students in the class. In doing so, each student will complete all three stages of a statistical analysis: collect data, organize data, and analyze data. A fun segment of this assessment is the opportunity to compare our data to data describing the vertical jumping ability of professional athletes.

Step_1: The first step of the project is to collect perceptual data regarding what the students in the class think about how “good” their vertical jump is. Due to the fact that many students have never calculated their vertical jump, many students will not know what a good vs. bad vertical jump is. Therefore, the perceptual data could be very misleading when compared to the findings later on in the study.

Once a class poll is taken regarding if students feel that they have a good vertical jump, students will calculate the joint, conditional, and marginal relative frequencies.

Step_1.png

Investigation

1 minutes

For this section of the investigation, students will be working in heterogeneous groups of 3-4 of their peers to collect and organize the first sets of data. Students will need to work within their groups to choose appropriate tools to calculate the height, reach height, and vertical jump of their group members.

Step_2: In this step, students work in their groups to calculate height, reach height and vertical jump of all of their group members and record their findings in the table on their worksheet. While this portion of the lesson can get slightly chaotic, I usually choose one or two groups to go out into the hallway to perform their calculations. This tends to cut down on the noise in the classroom.

Once all of the groups have collected their data and organized it into the table we come back together to make a table for the whole class. Note: If it will cause a problem or distraction to have students vertical jump results posted (due to embarrassment) I have had students enter the data into a table under simply male 1, male 2, male 3, etc. so that no student names are actually attached to the data. This can be done anonymously while groups are finishing collecting their data.

Students finish with step 2 by calculating the mean and five number-summary for the entire class’ vertical jump heights.

Step_3: At this point, I reassemble the students into pairs due to the fact that too many students in a group can be counterproductive for the remainder of the project and I always like students to have one other person to critique and analyze their ideas.

Now that students have collected all of the data on vertical jumps for both males and females in the class they can display the data in a side-by-side box plot. When students are writing their conclusion statement it should become clear how well they have understood the concepts. Students should not only make surface level observations but should try to make insightful generalizations by citing specific evidence from their box plot and data tables. Scaffolding: For some of my students who struggle, I will look over their data and use a highlighter to mark 3-5 numbers that they should mention in their conclusion. Often, the choice of which numbers are the important ones to cite can be overwhelming for students. I try to work with them to determine the numbers that are most important and we have a dialogue as to why.

Step_4: In step 4, we bring a cart of laptops to the room or travel to the computer lab depending on the availability of technology. It is important that each pair of students has access to one computer. I like to have students work in pairs on this section as well because students often like to share their findings and it is good to have another student to help make decisions of which athletes to use.

Students can use the given websites as a place to start but often know of other places to find such data. Extension: While it is not required for this portion, I may encourage some pairs of students to research the height of the professional athletes as well so that they can construct a scatter plot for the professional athletes as well in step 6.

Step_5: Once students have ample time to collect the data on the vertical jump of professional athletes, they use their findings and the data from our class to construct two side-by-side box plots. The expectation of the conclusion statement in this section is similar to that in step 3. In this section while the vertical jumps of the professional athletes will be greater than the students in the class, students should also be encouraged to discuss the spread of the data in both box plots. Students should also make comparisons between the spread of the data for both males and females. This is also a good question to ask students to discuss the mean and the median for their data sets and determine which is a better measure of “center”.

Step_6: In step 6, students will investigate another statistical question that deals with bivariate data. Students can re-visit the data collected for the entire class with each student’s height, reach height and vertical jump height. Students will construct a scatter plot of the data and determine if there is any correlation.

In parts b and d students will be informally analyzing the residuals of the graph to determine how well their prediction equation fits the data. They can also verify this using technology. Note: If a weak correlation is found, the slope found in part c may not carry much meaning. However, it is important that students try to understand the slope of the graph in the context of the particular data.

Extension: Students who actually collected data on the heights of the professional athletes that they researched (see part 4) do not have to hypothesize about part e, they can actually construct another scatter plot to determine the correlation and line of best fit. Other students can try to make a generalization based off of a hypothesis.

stats_project.docx

stats_project.pdf

Step_2.png

Step_3.png

Step_4.png

Step_5.png

Step_6.png

Closure

20 minutes

Step_7: In this step, students summarize what they have learned as a result of completing this study. Parts a and b in particular have a reflective component which requires students to think about their own learning and reflect on what they have learned and what they thought before beginning the study. In part c, students have the opportunity to make improvements to the work and expand any limitations in order to extend the work to a more broad population.